The multiple Olympic champion and first-ever British winner of the Tour de France said he also decided to accept the honour in 2013 after he got the blessing of his rock star hero Paul Weller.
Sir Bradley made the comments on BBC Radio 4’s Desert Island Discs when he also told presenter Kirsty Young about how the way he was abandoned by his father when he was a toddler has never left him and how his mother made extreme sacrifices to help him pursue his Olympic cycling dreams.
Asked about the knighthood, he said: “It was quite strange actually. I never saw myself as a Sir or anything.
“I remember I said to my Nan I wasn’t going to accept it. My granddad had died in 2010 and she said, ‘You’re stupid, you’re bloody crazy, you’ve got to accept it - George would turn in his grave if you turned that down’ and I sort of saw it from my Nan’s point of view.
“She must have remembered when I was a baby in that flat. Where we grew up, there’s not many people who become Knights of the Realm. I never use it. People use it, but I never use it.”
Sir Bradley said he also thought about the inspiration he would have had as a child if a knight had come to his school and told him about winning the Tour de France.
“It’s that inspiration thing,” he said.
Sir Bradley said has father Gary’s decision to leave him when he was 18 months old has always cropped up in his life.
“He abandoned us,” he said. “It’s never left me and it will continue to stay with me for the rest of my life.”
Gary Wiggins was an Australian “hard man” cyclist who moved back to his native country after his relationship broke down with Wiggins’s mother, Linda.
He talked about how his father dealt drugs to other cyclists and confirmed the story that he used his young son’s nappy to smuggle amphetamines through customs.
Sir Bradley described how he finally made contact with his father when he was 18 and later met him in Australia. Gary Wiggins was murdered in 2008.
He said: “He was living in a caravan park and didn’t have a lot to his name - banned from driving, every now and again he’d just go off on one and drink himself into a stupor. He kept going on about how he wanted to make up for the 18 years. It suddenly dawned, not so much at that age but when I had my own son, not only the child - ‘how could you leave and not have any contact or wonder at some stage what he’s up to?’ - but for my mother as well - just leaving without any word, or money and anything.”
Sir Bradley said he thinks about what his father did most when he is with his own son.
Asked about his qualities as a father, Sir Bradley said: “Just be there for them every step of the way”.